If you're overpaid, the employer has the legal right to demand that you repay the money. If you try to hang on to the money, the company could take court action, through the civil courts, to get it back. They could also treat it as a disciplinary offence. Additionally, retaining property (including money) given to you in error, is a criminal offence under the Theft Act.
Most companies will be sympathetic if you tell them that you can't afford to repay the money in a single payment. It's usually possible to make arrangement to pay back a small amount each week (or month, as appropriate).
The foregoing applies to over-payments. If you were off sick, your employer should have paid you Statutory Sick Pay. (There's no obligation to pay more than that, unless there's a specific provision in your contract). So they should only be reclaiming the difference between full pay and SSP, not every single penny they paid you.
Chris